Multicut decomposition methods with cut selection for multistage stochastic programs

TL;DR

This paper presents CuSMuDA, an improved multicut decomposition algorithm with cut selection for multistage stochastic linear programs, demonstrating significantly faster solution times across various portfolio and inventory management problems.

Contribution

The paper introduces CuSMuDA, a novel variant of MuDA that incorporates cut selection strategies, with proven convergence and enhanced computational efficiency.

Findings

CuSMuDA converges in a finite number of iterations.

CuSMuDA is 5.1 to 12.6 times faster on portfolio problems.

CuSMuDA is 6.4 to 15.7 times faster on inventory problems.

Abstract

We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates strategies to select the most relevant cuts of the approximate recourse functions. We prove the convergence of the method in a finite number of iterations and use it to solve six portfolio problems with direct transaction costs under return uncertainty and six inventory management problems under demand uncertainty. On all problem instances CuSMuDA is much quicker than MuDA: between 5.1 and 12.6 times quicker for the porfolio problems considered and between 6.4 and 15.7 times quicker for the inventory problems.